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Spline-backfitted kernel smoothing of additive coefficient model. (English) Zbl 1186.62134

Summary: The additive coefficient model [L. Xue and L. Yang, Stat. Sin. 16, No. 4, 1432–1446 (2006; Zbl 1109.62030); J. Stat. Plann. Inference 136, No. 8, 2506–2534 (2006; Zbl 1090.62041)] is a flexible regression and autoregression tool that circumvents the “curse of dimensionality”. We propose spline-backfitted kernel (SBK) and spline-backfitted local linear (SBLL) estimators for the component functions in the additive coefficient model that are both (i) computationally expedient so they are usable for analyzing high dimensional data, and (ii) theoretically reliable so inference can be made on the component functions with confidence. In addition, they are (iii) intuitively appealing and easy to use for practitioners. The SBLL procedure is applied to a varying coefficient extension of the C. W. Cobb and P. H. Douglas model [Am. Econ. Rev. 18, 139–165 (1928)] for the U.S. GDP that allows nonneutral effects of the R&D on capital and labor as well as in total factor productivity (TFP).

MSC:

62P20 Applications of statistics to economics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
65C60 Computational problems in statistics (MSC2010)
62G05 Nonparametric estimation
62H12 Estimation in multivariate analysis
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